How I Teach the Midpoint and Distance Fomula


I know it's crazy, but I love teaching the distance and midpoint formulas in Geometry.  They're largely procedural, and the kids hate them, but for some reason, I like it.  Also, this is the first lesson of the year where my kids finally see my crazy side.

This is a cute way to help students remember the midpoint and distance formulas!  This activity really helps my high school geometry students remember the lesson.

First, the distance formula…
I talk to the kids about the distance formula, we talk about how it could be useful, and where it comes from, etc.  However, I have found that my students always seem to have trouble remembering the actual formula.  So, the first time I write the formula down I tell them about the "face" of the distance formula.  

The distance formula has the face of a girl.  She has long hair, but she always pulls it to the side.
How I Teach the Midpoint and Distance Formulas

These are her eyes.
How I Teach the Midpoint and Distance Formulas

She also has very long eye lashes.
How I Teach the Midpoint and Distance Formulas

These are the pupils in her eyes.
How I Teach the Midpoint and Distance Formulas

This is her nose.
How I Teach the Midpoint and Distance Formulas

And in the alphabet, x comes before y.
How I Teach the Midpoint and Distance Formulas

Then, for each example we work together I have the kids talk me through the face on each problem.  It takes me less than 60 seconds to talk about the face, but the kids remember it.  Whenever a student asks for the formula, inevitably someone will say "Remember the face!".  I'll chalk that up as a win.

Second, the midpoint formula…
I talk to the kids about the formula and the usefulness again.  Then, I show them the cheer and I make them stand up and repeat it with me.  I found an example on YouTube that you can see below.


"Midpoint, midpoint, what do you do?  Add them together and divide by two!"

The kids think these are totally cheesy, but it does seem to help them remember.  Also, the cheesiness helps break up an otherwise boring lesson.  Bring on the cheese!

I taught this lesson on a block day, so I had plenty of time for activities and review after the lesson.  The distance formula always seems to be a little more troubling for students, so I had them complete a Distance Formula Partner Worksheet to practice.  When they were finished, they completed the Midpoint and Distance Formula Stations Maze.  This was the first time that I've used a stations maze this year, so I explained the directions very slowly and clearly.  I use them all the time, so I won't have to give directions again.  My students finished both pretty quick, but I do have honors students.

Bellwork Keeps Me Sane

I call warmups "Bellwork".  I heard it once and thought it was cute.
Bellwork - work you do when the bell rings.

Why do I use bellwork activities for high school students?  Warmups, bell ringers, or whatever you call them, save my sanity!

I am very strict about my beginning of class routine.  My kids come in, check their homework, and start their bellwork.  I'm "so mean" that I even expect them to start working before the bell rings (or so I've been told).  Once their bellwork is finished, I'm usually ready to start class.  It's a personal pet peeve when kids are noisy at the beginning of class.  I also need to take attendance and check their homework.

90% of the time, this is what you will see:
  • Kids walk in and pick up the key for the previous night's homework.
How Bellwork Saves My Sanity Each and Every Class Period  |  mrseteachesmath.blogspot.com
  • They check their homework while I walk around and check it for completion.
  • Then, the kids put their homework key away and get their notebook out of the cabinet.
How Bellwork Saves My Sanity Each and Every Class Period  |  mrseteachesmath.blogspot.com
  • Then, they work on their bellwork and put away their notebook when they're finished.
Since they start before the bell rings, they are totally done with this within the first 5-7 minutes of class.  Sometimes, I plan for the bellwork to take a little longer so that I can give them review time.  Other times, I make it very short so that we can get started as soon as possible.

This works for me.  It makes the beginning of every class smooth.  It gives me a mental "reset" if the previous class period was stressful.

Bellwork.  I'm a huge fan.


What does your beginning of class routine look like?






First Day of School Activities

I can’t believe that today was the first day of school!  This summer FLEW by for me.  

I’ve never done anything fantastic on the first day of school.  I usually have the students go around the room and introduce themselves, go over the syllabus, etc.  Ugh, I hate it.  This year I decided to do something totally different.  My goal was for the kids to start working and thinking, without actually starting my curriculum.  We only have 30-minute classes on the first day of school, so I don’t have a lot of time.

First, my students came in and found their desks.  I printed their names on strips of paper so that I could easily assign seats.

Their bellwork was posted on the board.  My kids even have bellwork on the first day.  I used this sheet for their bellwork, whatever they didn’t finish was homework.

Free First Day of School Activity

Mrs. E Teaches Math:  First Day of School Questionnaire - free download

This year I’m teaching Geometry Honors and Algebra 2 Honors.  My honors kids (and their parents!) would have a heart attack if I didn’t give the syllabus on the first day and talk about expectations.  So, I handed it out and talked about it for maybe 5 minutes.  I also handed out the calendar for the first unit.

Then, the fun began!  I decided to use two brain teasers that I found on Stella's Stunners.  You can find them here and here.  They looked like this:
Mrs. E Teaches Math:  First Day of School Questionnaire - free download
Mrs. E Teaches Math:  First Day of School Questionnaire - free download

I liked using these brain teasers because I could make them take as much (or as little) time as I needed!

When there were a little more than 5 minutes left in class, I quickly wrapped up and introduced the idea of an exit ticket.  I don’t know if any of my students have done them before.  I had them write a Tweet using #Mathis as their inspiration.  I totally ripped this idea off of Sarah Hagan at Math = Love.  I made my own paper for the kids to write their Tweets on.  I wanted something to help them count the characters, but some of my freshman can’t write in little boxes to save their life, so I just gave them blanks to write on.   I had three kids ask me what Twitter was.  #Facepalm  #TeacherFail  I told them to just to fill in the blank:  Math is _______.  I totally love how cute it turned out!  I hung some on the wall.  I would have used too much tape hanging 70+ Tweets.

Mrs. E Teaches Math:  First Day of School Questionnaire - free download

Here are some of the funniest/best Tweets.  Anytime a student used their name I changed it to their initials :)
Mrs. E Teaches Math:  First Day of School Questionnaire - free download
I think it's gonna be a good year!

First Year Flashback


It’s always fun to think back to your first year teaching.  I made so many mistakes, but I also did some great things!

What ago group and subject were you teaching?

I taught Geometry (9th and 10th grade) and Algebra 2 Honors (10th grade).

What was your first classroom like?

My school was being rebuilt my first year, so I was in a portable.  Everything was a pinkish beige, including the tile floor.  I learned the hard way that the white boards did not erase.  So, I used the document camera to project everything onto the white board.  My classroom was so empty, because I knew I would be moving into a new building the next school year.  I think I hung three posters.

Were you given supplies or materials?

My school is great about supporting new teachers.  I has a great mentor that made sure I was supported and ready to go when school started.  She and I even when on a shopping trip to a teacher’s supply store together.  My team members gave me their entire curriculum during inservice.  I could use it or come up with my own thing, but it was fantastic to have a safety net.  It was a huge relief and allowed me to actually have a life my first year.  After that positive experience, I will always help new teachers in my school in this way.

I had a few supplies in my room (a stapler and tape), but there was a large storeroom for the teachers.  I don’t remember having to buy anything.

What was the hardest part of your first year teaching?

I made several lessons harder than they needed to be.  So, I guess the hardest part was explaining things so that students could understand.  I think back to some of my explanations my first year and I cringe!  The first time I taught multiplying matrices, it BOMBED.  Now, I teach it using different colors for each entry in the matrix and I don’t have to explain it more than once.  So much better!

What was the best part of your first year teaching?

My colleagues, by far.  My mentor helped me so much and really helped me realize how to channel my creative ideas to work in the classroom.  We even wrote a lesson plan together and taught it on the same day.  Doing that gave me the confidence to try trashketball in my classroom for the first time.  Also, my department chair and whole department were very supportive.

What do you know now that you wish you knew that first year?

It won’t be perfect, but that’s ok.  You will have lessons that bomb, your classroom management won’t be perfect, you will forget something important, you will stay up late working…  However, it’s just your first year!  Cut yourself some slack!  Also, put your work away and go to bed early!


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